1. linear equation

Hi,

A linear equation can be represented as:

y=mx+b
Ax+By+C=0

I can't understand these equations.

1 - In the case y=mx+b, what the y variable represents?
If m represent the slope, and b the place where the straight line crosses the yy axis, what the y means?

For example, m=1, x=2 and b=3:
y=1*2+3=5.

What the number 5 means?

2 -
How can I draw a line in the graph that satisfies that Ax+By+C=0?

3 -
What's the purpose of the variable A, B and C?

Thanks,

2. Originally Posted by pedrosacosta
Hi,

A linear equation can be represented as:

y=mx+b
Ax+By+C=0

I can't understand these equations.

1 - In the case y=mx+b, what the y variable represents?
If m represent the slope, and b the place where the straight line crosses the yy axis, what the y means?

$\displaystyle \color{red}\mbox{Like in ANY other function, the y and x represent a certain relation between}$ $\displaystyle \color{red}\mbox{the cooordinates of any point}$$\displaystyle \color{red}\mbox{ in the xy-plane belonging to the graph of the function}$

For example, m=1, x=2 and b=3:
y=1*2+3=5.

What the number 5 means?

$\displaystyle \color{red}\mbox{means that y=5 when x=3, or what is the same:}$ $\displaystyle \color{red}\mbox{ the point (3,5) in the xy-plane belongs to the straight line}$ $\displaystyle \color{red}\mbox{whose equations is y = x + 3}$

$\displaystyle \color{red}\mbox{Note that y=x+3 really means that ANY point on the line}$ $\displaystyle \color{red}\mbox{ can be expressed as (x,x+3)}$

2 -
How can I draw a line in the graph that satisfies that Ax+By+C=0?

== Choose at least two different values for x and after plugging each of them in the equation find the corresponding values for y, this way you get two points on the line and you can join them with a straight line.

3 -
What's the purpose of the variable A, B and C?

== To determine the relation between the x-coordinate and the y-coordinate of each point of the plane belonging to the line

Tonio

Thanks,
.